Exercises: Module 04 — Unsupervised Learning¶

Instructions¶

All exercises use scikit-learn and numpy unless otherwise noted.

Easy Exercises (1–3)¶

Exercise 1¶

Difficulty: Easy Objective: Apply k-means and choose k

Load the make_blobs dataset with 5 centers. Run k-means for k=2 through k=8. For each k, compute the silhouette score and inertia. Identify the correct k.

Exercise 2¶

Difficulty: Easy Objective: Apply PCA for variance analysis

On the digits dataset (64 features), apply PCA. Print the cumulative explained variance ratio. How many components are needed to explain 90%, 95%, and 99% of variance?

Exercise 3¶

Difficulty: Easy Objective: Compare clustering algorithms

On the moons dataset (make_moons), apply k-means and DBSCAN. Compare their cluster assignments visually (print cluster counts) and quantify with ARI (adjusted rand index) against ground truth.

Medium Exercises (4–6)¶

Exercise 4¶

Difficulty: Medium Objective: PCA + supervised learning pipeline

On the digits dataset: train logistic regression on raw features, then train on PCA-reduced features (keep 95% variance). Compare test accuracy and training time. Does dimensionality reduction hurt accuracy?

Exercise 5¶

Difficulty: Medium Objective: Anomaly detection with DBSCAN

Generate a dataset with 200 normal points (Gaussian cluster) and 20 anomalies (uniform random in a wider range). Apply DBSCAN with appropriate parameters to identify the anomalies. How many anomalies does DBSCAN correctly identify?

Exercise 6¶

Difficulty: Medium Objective: Silhouette analysis

For the wine dataset (no labels visible to the algorithm), run k-means for k=2 through k=6. Plot (or print) per-cluster silhouette scores for each k. Which k gives the most balanced, high-silhouette clusters? How does this compare to the true k=3?

Hard Exercises (7–8)¶

Exercise 7¶

Difficulty: Hard Objective: Implement k-means from scratch

Implement k-means in numpy without sklearn. Your implementation must: - Initialize centroids using k-means++ (not random) - Iterate until convergence or max_iter - Return final labels and final WCSS

Verify your results match sklearn.cluster.KMeans on make_blobs.

Exercise 8¶

Difficulty: Hard Objective: PCA for noise filtering and reconstruction

On the MNIST digits (or digits dataset), apply PCA, keep the top k components, and reconstruct the data. Compute reconstruction error (MSE) for k = 5, 10, 20, 50, 64. At what k does reconstruction become visually acceptable?

Expert Exercise (9)¶

Exercise 9¶

Difficulty: Expert Objective: Implement a linear autoencoder and compare to PCA

Build a simple autoencoder using PyTorch (2-layer encoder, 2-layer decoder) on the digits dataset with a bottleneck of 2 dimensions. Train with MSE reconstruction loss for 100 epochs. Compare: - Reconstruction MSE vs. PCA with 2 components - Visualization: scatter plot of latent space (color by digit class) vs. PCA 2D projection - What does the autoencoder learn that PCA cannot?